Curved beam model of the proximal femur for estimating stress using dual‐energy x‐ray absorptiometry derived structural geometry

Abstract

The investigation of individual differences in hip strength requires a method to measure structural geometry in vivo and a valid analytical approach to calculate mechanical stress. We developed a method for deriving structural geometry of the femur from the proximal shaft through the femoral neck, using data from dual energy x‐ray absorptiometry. The geometric properties are employed in a two‐dimensional curved beam model of the proximal femur to estimate stresses on the lateral and medial bone surfaces. Stresses calculated by this method are compared with those from the conventional flexure formula and with results produced from a cadaver femur with use of three‐dimensional finite element analysis of computed tomography data. Loading conditions simulating a one‐legged stance and a fall on the greater trochanter are employed. Stresses calculated by curved beam theory are in much better agreement with three‐dimensional finite element analysis than are those for which the conventional straight beam formula was used. In simulation of a fall on the greater trochanter, all three methods show peaks of stress at the femoral neck but only the curved beam and finite element analysis methods show an additional peak at the medial intertrochanteric margin. Both neck and trochanter regions correspond to common failure sites for hip fractures in the elderly. The curved beam treatment of hip structure derived from dual‐energy x‐ray absorptiometry provides an approach for the in vivo engineering analysis of hip structure that is not practical by other methods.